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SPATIAL QUERY PROCESSING
USING VORONOI DIAGRAMS
by
Mehdi Sharifzadeh
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(COMPUTER SCIENCE)
May 2007
Copyright 2007 Mehdi Sharifzadeh

Spatial query processing in spatial databases, Geographic Information Systems (GIS), and on-line maps attempts to extract specific geometric relations among spatial objects. As a prominent category of spatial queries, the class of nearest neighbor queries retrieve spatial objects that minimize specific functions in terms of their distance to a given object (e.g., closest data point to a query point). The most efficient algorithms that address nearest neighbor queries utilize the R-tree index structure to avoid I/O operations for the groups of data objectsthat do not contain the final query result. However, they still result in unnecessary I/O operations as R-trees are not efficient in elaborate exploration of the portion of data space thatincludes the result.; In this dissertation, we propose a new index structure, termed VoR-tree, that incorporates Voronoi diagrams into the R-tree index structure for I/O-optimal processing of nearest neighbor queries on point datasets. The neighborhood information encoded in Voronoi diagrams allows a VoR-tree-based algorithm to optimally explore the data space towards the result. We complement our efforts by proposing I/O-optimal algorithms for k nearest neighbor, reverse k nearest neighbor, k aggregate nearest neighbor, and spatial skyline query types. These algorithms perform the least amount of I/O with respect to the information provided in their underlying VoR-tree. Therefore, they find the query result with less I/O operations than their best competitor for each query type.

SPATIAL QUERY PROCESSING
USING VORONOI DIAGRAMS
by
Mehdi Sharifzadeh
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(COMPUTER SCIENCE)
May 2007
Copyright 2007 Mehdi Sharifzadeh